Question

A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.

Answer 1

For a large cylindrical vessel,

Height = H = 24 cm

Radius = R = `40/2` = 20 cm

∴ Volume of large cylindrical vessel = πR²H

= (π × 20 × 20 × 24) cm³

For each small cylindrical bottle,

Height = h = 10 cm

Radius = r = `8/2` = 4 cm

∴ Volume of each small cylindrical bottle = πr²h

= (π × 4 × 4 × 10) cm³ 

Now, number of small cylindrical bottles which can filled

= `"Volume of large cylindrival vessel"/"Volume of each small cylindrical bottle"`

= `(pi xx 20 xx 20 xx 24)/(pi xx 4 xx 4 xx 10)`

= 60